Question

qual é a soma dos numeros impares compreendidos entre 1001 e 10101 ?

Answer 1

a_1 = 1003
a_n = 10099
r = 2
n = ?
S_n = ?

 Encontremos a quantidade de termos,

$a_n=a_1+(n-1)r\\10099=1003+(n-1)\cdot2\\2(n-1)=9096\\n-1=4548\\\boxed{n=4549}$
 
 Por fim,

$S_n=\frac{(a_n+a_1)n}{2}\\\\S_n=\frac{(10099+1003)\cdot4549}{2}\\\\S_n=\frac{11102\cdot4549}{2}\\\\\boxed{\boxed{S_n=2.5251.499}}$